Probabilistically nilpotent hopf algebras

Miriam Cohen, Sara Westreich

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper we investigate nilpotenct and probabilistically nilpotent Hopf algebras. We define nilpotency via a descending chain of commutators and give a criterion for nilpotency via a family of central invertible elements. These elements can be obtained from a commutator matrix A which depends only on the Grothendieck ring of H. When H is almost cocommutative we introduce a probabilistic method. We prove that every semisimple quasitriangular Hopf algebra is probabilistically nilpotent. In a sense we thereby answer the title of our paper Are we counting or measuring anything? by Yes, we are.

Original languageEnglish
Pages (from-to)4295-4314
Number of pages20
JournalTransactions of the American Mathematical Society
Volume368
Issue number6
DOIs
StatePublished - 1 Jun 2016

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